Product quality during shipping by generating lane temperature and product temperature from models

ABSTRACT

Systems and methods for modeling a temperature in a thermal package in a lane of commerce using forecast weather data or estimating the actual temperature history in a thermal package using actual weather data. Lane temperature is recognized and used as an intermediate calculated variable derived from weather data. Machine learning techniques estimate the lane temperature to determine a model. Product temperature in thermal packaging is estimated by simultaneously solving a set of heat transfer equations. The above is used to with forecast weather data to calculate a lane temperature and then calculate an expected product temperature based on the time and date of shipment. This product temperature curve is then analyzed with a set of decision rules to improve decision making on when to make a shipment and the best packaging to use.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a division of U.S. patent application Ser. No.16/786,136, filed Feb. 10, 2020, entitled “Product Quality DuringShipping by Generating Lane Temperature and Product Temperature fromModels,” and claims priority to U.S. Provisional Patent Application No.62/803,770, filed Feb. 11, 2019, entitled “Methods for Using Weather,Lane, and Package Data to Improve Logistics Decision Making for HighValue Temperature Sensitive Product,” the disclosure of each isincorporated herein by reference in its entirety.

BACKGROUND OF THE INVENTION

Shipping temperature sensitive products is an everyday occurrence,whether it is pharmaceuticals, foods, electronics, or many otherproducts. When shipping these items, the industries rely on insulatedpackaging, heat sink materials, phase change materials, and/or activecooling and heating to protect the product. In addition, many of theseshipments include temperature monitors to record the temperatures theirproducts experience while shipping. These temperature monitors can thenbe used to confirm that the appropriate temperature was maintained inthe packaging.

Companies can look at weather data to see what the weather is at anorigin, destination, and everywhere in between for a shipment. However,the container is not directly exposed to these weather conditions whenbeing shipped. The reason for this difference is that a container isoften not just left outside, it is shipped on the inside of planes,trains, and trucks which have their own unique set of conditions in thecargo areas. As a result, there is a “lane temperature” that isexperienced by a container, which is the temperature it actuallyexperiences when shipped from an origin to a destination. The lanetemperature is not completely independent of the weather temperature,but they are significantly different.

Many of the currently available solutions for shipping temperaturesensitive product are overdesigned for their purpose, which increasesshipping costs considerably. For example, an insulated package that isdesigned to maintain refrigerated temperature for twenty-four hours inthe heat of summer is unneeded when it is used in early spring. Whendeciding what to use for shipping temperature sensitive products, acompany selects a container that has been tested against the worst-caseconditions for that time of year and route of travel. While this gives ahigh degree of confidence that the product maintains the correcttemperature, it means the solutions are not experiencing anything closeto the extreme conditions for which they are designed. A container maybe qualified against the hottest summer day on record, but thatcontainer will be used on a relatively cool day on the last day ofsummer as well.

A specific industry example is the use of ISTA 7E for qualification ofpassive thermal packaging for the biopharma industry. The temperatureprofile for ISTA 7E is based on the 95% confidence interval of thehottest two weeks and coldest two weeks of the year in the United Statesfor shipping lanes throughout the United States. The end result is apackage designed to maintain temperature for 48 hours based on the ISTA7E thermal profile is overdesigned for 48 weeks out of the year. To meetthe strict criteria to work in the limited circumstances set by the ISTA7E thermal profile, the packaging has more insulation and more phasechange material than is needed for the majority of the year; yet thepackage is used as designed during times it is not needed. That extrainsulation and phase change material results in higher packaging andshipping costs.

The standard for heat transfer modeling of thermal packaging is finiteelement analysis. These models use numerical methods to solve complexheat transfer processes through the use of steady state calculationsover small time periods and short distances. To ensure good accuracy andstability of the simulation, the models will commonly use a ‘grid’overlay for the package that contains more than one million points andcalculate the resulting million plus steady state equations once persecond. This is a significant calculation burden that hurts the abilityto run numerous models quickly. In some cases it can take hours to run asingle model. As a result, these calculations are typically only usedwhen designing a container, as any other application requires a fasterresponse from a model.

BRIEF SUMMARY OF THE DISCLOSURE

The present disclosure improves upon the current state of shipping oftemperature sensitive products. First, lane temperature is recognizedand used as an intermediate calculated variable derived from weatherdata. This eliminates the problem with conventional analysis of usingthe weather temperature as a poor proxy for the actual temperature(s) apackage is exposed to in the lane of commerce. Second, machine learningtechniques are used to customize the shipping lanes to estimate the lanetemperature, which improves the results enough for the ‘weather to lanemodel’ to provide usable results. Third, the present disclosure presentsan elegant solution for the complex heat transfer problem of estimatingproduct temperature in thermal packaging. The solution uses a differentapproach to the heat transfer equations, by not using the grid methodand instead using a pseudo geometry to simplify the calculations. Thisresults in simulations that can be run in seconds instead of hours.

The sum of these key technology discoveries allows us to take forecastweather data for an origin and destination, calculate a lanetemperature, and then calculate an expected product temperature based onthe time and date of shipment. This product temperature curve is thenanalyzed with a set of decision rules to improve decision making on whento make a shipment (to avoid temperature extremes) and the bestpackaging to use (to take advantage of lighter, cheaper packaging inmild weather).

In accordance with the present disclosure, there is provided a methodfor modeling a temperature in a thermal package in a lane of commerce.The method includes receiving weather data; selecting a weather model inaccordance with an origin of a shipment, a destination of the shipment,and a date and a time of the shipment; determining an estimated lanetemperature for the shipment using a selected weather model, wherein theestimated lane temperature is an estimate of a temperature it actuallyexperienced by the thermal package between the origin and thedestination; determining a product temperature using a package model inaccordance with the estimated lane temperature; determining a packagingto be used for the shipment from the product temperature; and displayinga determined packaging in a user interface.

In accordance with another aspect of the disclosure, there is provided amethod modeling a thermal package's heat transfer. This further methodincludes using a pseudo-geometry that represents three heat transferprocesses in a thermal package that include (1) product to phase changematerial (PCM), (2) ambient temperature to product, and (3) ambienttemperature to PCM; for each of the three heat transfer processes:positing a solution of a partial differential equation as a first orderplus dead time (FOPDT) model having a gain coefficient, a time constant,and a dead time that change as the PCM in the thermal package changephase; and simultaneously solving the three heat transfer models andadjusting the gain coefficient, the time constant, and the dead timeconstants for subcooled PCM, PCMs that are changing phase, and PCMs thathave fully changed phase; and using a result to generate a package modelthat receives product temperature and lane temperature data to determinean optimal packaging from a predetermined set of packing to be used fora shipment of the product.

Other systems, methods, features and/or advantages will be or may becomeapparent to one with skill in the art upon examination of the followingdrawings and detailed description. It is intended that all suchadditional systems, methods, features and/or advantages be includedwithin this description and be protected by the accompanying claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing summary, as well as the following detailed description ofvarious and several implementations, is better understood when read inconjunction with the appended drawings. For the purpose of illustratingthe disclosure, there is shown in the drawings example constructions ofthe implementations where like elements have like reference numerals;however, the disclosure is not limited to the specific methods andinstrumentalities disclosed. In the drawings:

FIG. 1 is an overview of an environment in which the present disclosuremay be implemented;

FIG. 2 is a flow chart that further details of processes performed in102 of FIG. 1 ;

FIG. 3 is a flow chart that further details of processes performed in104 of FIG. 1 ;

FIG. 4 is a flow chart that further details of processes performed in106 of FIG. 1 ;

FIG. 5A is a flow chart that details the development of the processperformed in 102 of FIG. 1 ;

FIG. 5B is an example structure of the machine learning neurons in setlayers;

FIG. 6 is a flow chart that details the development of the processperformed in 104 of FIG. 1 ;

FIG. 7 is a flow chart that describes an example pseudo-geometry andstage decider used in the development of the process performed in 104 ofFIG. 1 ; and

FIG. 8 is a flow chart that details the development of the processperformed in 106 of FIG. 1 .

DETAILED DESCRIPTION Overview

The present disclosure is directed to systems and methods for modelingthe temperature in a thermal package in a lane of commerce usingforecast weather data or estimating the actual temperature history in athermal package using actual weather data.

As shown in FIG. 1 , there is illustrated a high-level overview andoperation flow of a system 100 in which the present disclosure may beimplemented. The system 100 may include one or more databases (101, 103,105), as described below, where the weather data, lane temperature data,and the product temperature data are stored. A client, through a humanmachine interface (HMI), queries a server (system 100) to complete a setof scenarios. The server queries the databases for the relevantinformation, then inputs them into the model for calculation. The serverthen provides the results from the scenarios to the client.

The operational flow of FIG. 1 begins with weather data being downloadedthrough an API from a supplier of weather data and stored in weatherdata storage 101. The weather data may take any known format, includingbut not limited to excel (xlsx), comma separated values (csv), or text(txt) file formats.

A weather model 102 extracts data from the Weather Data Storage 101based on origin, destination, date, and time of the shipment. The modelthen calculates the estimated lane temperature for that specificshipment by inputting the weather variables into a machine learningalgorithm. Further details of the operations performed by the weathermodel 102 are described with reference to FIG. 2 . The lane data is thenstored in the Lane Data Storage 103. Lane Data Storage 103 may be adatabase which contains historical lane data and lane data estimates.

The package model 104 operates to extract data from the lane temperaturestorage 103 based on the shipment details. The package model 104 thencalculates the estimated product temperature for that specific shipmentusing a first order plus dead time model. Further details of theoperations performed by the package model 104 are described withreference to FIG. 3 . The product temperature data is stored in theproduct temperature storage 105. Product temperature storage 105 may bea database which contains historical product temperature data andproduct temperature estimates.

Data from the product temperature storage 105 is then provided to adecision model 106 that applies rules to determine when to make ashipment and/or the best packaging to use for the shipment. Furtherdetails of the operations performed by the decision model 106 aredescribed with reference to FIG. 7 . The output of the decision model106 is provided to the HMI 107 for display to an end user. For example,the HMI 107 is a client-facing computer which will provide the resultsfrom the data analysis system 100.

In the operational flow and system 100 of FIG. 1 , the specific weathermodel to be used for a specific shipment in system 100 is selected basedon origin, destination, date and time of shipment, and service level forthe shipment. This specific model is developed using a weather modelcreation process 500 outlined in FIGS. 5A-5B. As will be describedbelow, the weather model is a machine learning model designed,developed, trained, and validated in the weather model creation process500. The package model is a mathematical, transfer function based modeldesigned, developed, optimized, and validated in a package modelcreation process 600. Finally, the decision model is a statistics-basedmodel designed, developed, optimized, and validated in a decision modelcreation process 700.

Weather Model (FIG. 2 )

Models may be used to make decisions about optimal packaging for a givenshipment. For example, if the user intends to ship a temperaturecontrolled package from an origin “A” to a destination “B” by two daycarrier, the user can look at the two day weather forecast for “A” and“B,” and then choose a package that is optimal for the expected lanetemperature during the shipment. This minimizes the overdesign that isin current use in the pharma industry. The weather model 102 can usepast, current, or forecasted weather data to estimate the lanetemperature during shipping.

With reference to FIG. 2 , at 201, weather data is initially downloadedfrom a server. The weather data may be received in a gridded format orother, as understood in the art. Additional information is received,such as the origin, destination, service level, date, and time of theshipment. At 202, a specific model is selected based on the additionalinformation. The details of the weather models are described below withreference to FIGS. 5A-5B. At 203, a query is then made to the weatherdata storage for information needed for the model in order to calculatethe lane estimate. This data is stored in the weather data storage 103.The data contains all weather data from previous shipments and currentweather data, such as temperature, cloud coverage, precipitation,surface air pressure, solar radiation, normal irradiance, horizontalradiation, pressure, wind direction, surface wind, surface dewpoint, wetbulb temperature, relative humidity, apparent temperature, wind speed,or many others. At 204, the data is then input to the weather model,which calculates a lane temperature estimate based on the data. Thisestimate is also stored in the weather data storage 103. The processends at 205.

Package Model (FIG. 3 )

With reference to FIG. 3 , at 301, the lane temperature, which is outputat 204 (see, FIG. 2 ) is provided to the package model. The packagemodel is a first order plus dead time model designed, developed,trained, and validated in the package model creation process. Thepackage model may use lane temperature estimates from past, present, orforecasted lane temperatures. At 302, the package model creates ascenario for the client. The scenario imports the lane temperatureestimate (from 301) and selects among available client-specifiedcontainers (304). Each container model is loaded individually, which mayuse the structure in FIG. 7 or other if there are several differentphase change materials (PCM) in the container. The models are a firstorder plus dead time (FOPDT) transfer function model, where thestructure and equation coefficients vary by the container. The containermodel loads the coefficients for the equations the govern each stage ofthat container, as well as the heat needed for the PCM to change phasefor the stage decider. The simulation for the container is run, and thenthe results are saved for evaluation in the decision model. After thescenario for a container is completed, the next container is loaded andsimulated. Once the model simulates all of the client's containers thescenario is completed. At 303, the results from that scenariocommunicated to the client.

Decision Model (FIG. 4 )

The output from the Package Model (104) is a time series data set thatmay be stored in Product Temperature Estimation Database (105). Thistime series data is associated with a particular package with aparticular origin and destination and service level shipped at aparticular time and date. The time and date can be in the future or inthe past. With reference to FIG. 4 , in the process 400, the output ofthe package model 104 and the client's specification for how risk-aversethey want to be are received as inputs. At 401, these inputs areextracted by a query, and at 402, a statistical calculation is made toevaluate the risk associated with each of the scenarios calculated at303 (see, FIG. 3 ). At 403, the results from step 402 are used in aclient specific evaluation. In an example case, the scenario couldclassify each container for that shipment in a low, medium, or high-riskclassification (404, 405, 406). In an example case, risk 404 could be anindication that unless there are extraordinary circumstances there is norisk to the product, risk 405 could indicate that the product may befine but cannot be given the little/no risk evaluation based on theclient's specification, and risk 406 could indicate that the productwill likely be harmed under most circumstances.

As an example case, the time series temperature data is compared to thetemperature specifications for the product. This allows the calculationof time out of temperature and maximum and minimum temperature for theproduct for that shipment.

Based on information from the product risk assessment, the maximumtemperature, minimum temperature, and total time out of temperature isconverted into a qualitative determination of the risk associated withthat shipment for shipments in the future, and a qualitativedetermination of product quality for shipments that have alreadyoccurred.

For shipments, the formula may take the form:

t _(out)→Qualitative assessment=low risk

t _(out) >t _(outspec) and T _(max) <T _(maxspec) and T _(min) >T_(minspec)→qualitative assessment=moderate risk

t _(out) <t _(outspec) and T _(max) >T _(maxspec) and T _(min) >T_(minspec)→qualitative assessment=high risk

where:

-   -   t_(out) is the total time outside of temperature    -   t_(outspec) is the specification for allowed total time out of        temperature    -   t_(max) is the maximum temperature is the data set    -   T_(min) is the minimum temperature in the data set    -   T_(maxspec) is the maximum allowable temperature in the data set    -   T_(minspec) is the minimum allowable temperature in the data set

The results of the decision model 106 are made available for access bythe human machine interface (HMI) (107).

Weather Model (FIGS. 5A-5B)

With reference to FIG. 5A, the development of the weather model beginsat 500 by receiving data (e.g., lane information) from the client. Byproviding the various inputs 501, the parameters for development can beset. This information can include information such as the origin,destination, service level, date, and time of shipment. Once theinformation is gathered to define the parameters of the model, aprotocol is written at 502 to gather data on the lane. This protocol mayinclude steps so that both the weather data and the lane data aregathered for a shipment with corresponding dates and times. This data issent to two storage locations, e.g., a weather database 503 and lanedatabase 504.

At 505, a neural network machine learning algorithm structure isgenerated to create the weather model. The neural network utilizes lossfunctions and optimizers to identify the ideal structure and parameters.The loss function calculates the difference between the estimatedtemperature and the validation set of data. The optimizer is a functionthat uses derivatives of the multi-dimensional surfaces to determine ifa variable needs to be more or less heavily weighed. The exact functionschosen for the machine learning algorithm will be determined as part ofthe optimization for a given data set, but in general the functions justdetermine how aggressively a solution is pursued and determine potentialerror.

The exact structure of the algorithm can be based on the algorithm'sevaluation of the best structure, or it can be set by the developer. Itmay be comprised of several layers of neurons, each which evaluate theinput from previous layers, and translate it into a single time seriesset of temperature data. It can also be in the form of a random forestmachine learning algorithm, of which there is no set initial structure.FIG. 5B is an example structure of the machine learning neurons in setlayers.

Many weather variables are available, but the model may only use theones that are important for that lane. In an example case, the weatherdata may contain measurements of temperature, cloud coverage,precipitation, surface air pressure, solar radiation, normal irradiance,horizontal radiation, pressure, wind direction, surface wind, surfacedewpoint, wet bulb temperature, relative humidity, apparent temperature,and wind speed. However, when the model is generated using the data itcan make determinations such as, “Wind speed is very important and willweigh more heavily in the calculations, but the wind direction hasalmost no effect on the temperature and will be weighed less heavily (ifat all).” The model is specific to an origin, destination, and servicelevel, as each one has slightly different methods of transport and thusdifferent reactions to each parameter. Some routes may be sent through aparcel network with several distribution centers, while others mightship via trucks straight to the destination.

Once the structure of the algorithm is set, data from the weatherdatabase 503 and the lane database 504 are provided as inputs as avalidation set for the evaluation of how good the model fits theexisting data. The training of the model, using the training data,allows the neural network to configure its internal parameters for flowof data information and values to and from the layers of neurons. Aftertraining, the model has a set of internal parameters for use.

At 506, data from the weather database 503 and the lane database 504 arefed into the weather model. Once completed, at 508, the algorithm thenoutputs the prediction. The algorithm performed at 506 can be refined at507 by gathering additional sets of data, which may result in changes tothe structure. If the weather model does not meet the validationparameters, the design is modified as needed (as described above) tomeet the validation parameters and the process returns to 506 where theprediction is output at 508. Next, results are compared to data setsfrom the weather database 503 and the lane database 504. At 509, anevaluation is made to determine if the current model structure issufficiently accurate. The weather model uses the validation data tocompare the results and determine if the model is adequate based onvalidation criteria and allowable tolerance. If the weather model is notadequate, then the protocol to gather data (at 502) may be changed orexpanded to collect more data. At 501, the results are then provided tothe developer.

Package Model (FIG. 6 )

With reference to FIG. 6 , the development of the package model beginsat 600 by writing a protocol to gather data sets. The protocol willgather product temperature data and lane temperature datacontemporaneously. This data is sent to a lane temperature storage 601and product temperature storage 602. At 603, a determination is made ifthe gathered data is sufficient for an accurate model.

In an example case, this determination can be made based on astatistical analysis of the available data, in addition to anyadditional data that is gathered. The model may consider the operatingerror of a container, the client's acceptable risk levels, and theactual temperature of the shipments that are being used for thevalidation sets. If the model data is considered sufficient, the data isused for the package model generation. The structure of the packagemodel may vary slightly between different types of containers, but theparameters of the equations to make the model can be estimated at 604using a system identification software. When the parameters are set, theadditional data sets are used at 605 as input for the model to evaluateits accuracy. At 606, a determination is made if the model issufficiently accurate. The model is considered accurate enough if theresults from the model are within a client's specified tolerance. Forinstance, a client may state their allowable tolerance is ±2° C. at alltimes from the actual temperature, or it may be that on average theerror over the whole shipment is ±0.5° C. The client will dictate thecriteria, and the model generation will account for it when determiningif it is sufficiently accurate. If the model is not consideredsufficiently accurate, and the original data collection protocol will bechanged or expanded to collect more data. If the model is consideredsufficiently accurate, the results are provided to the developer at 608.

Decision Model (FIG. 7 )

The decision model in accordance with an acceptable risk for theshipments. The development begins with determining a risk assessment(700). This risk assessment is usually product specific, but can begeneralized for all products that can be shipped. The risk assessmentgathers data such as the high and low temperature allowances anddurations allowed at temperatures outside that range. After conductingthe risk assessment, the tolerances are determined for how to evaluatethe model (701). These tolerances can be based on averages, movingaverages, maximum allowable difference from actual data, or othercriteria. Risk is calculated based on several different factors thatgive a statistical estimate of the results of the simulations. In anexample case, the variables that may be considered for evaluationinclude the confidence intervals of the weather forecast variables, theconfidence interval of the estimated lane temperature, and theconfidence interval of the estimated container temperature.

These criteria can be used alone or in combined based on, e.g., aclient's needs. The tolerances and product risks are combined todetermine the decision rules (702). In an example case, the decisionrules can be, “the product must stay between 2° C. and 8° C. for theentire duration, must be within 1° C. accuracy for every data point. Ifit is outside that temperature range it cannot go above 25° C. ever, andcan tolerate 10 hours at temperatures between 8° C. and 25° C.” Thegeneral form of the decision model is updated with the client specificcriteria, and the ways to evaluate and display risk are determined(703). The client may decide they want to display the risk results interms of low risk, medium risk, and high risk. In example cases, theserisk levels could be presented to a client in the form of a riskpercentage, a red/yellow/green evaluation, or as a simple yes/noresponse.

Each risk bracket is then determined using the combination of criteriaidentified above (704). After the client model is generated it iscompared to decisions that the client has made in the past forexcursions and evaluations (705). During their lifetime, mosttemperature sensitive products have shipments where an excursion hasoccurred. When these occur, from the temperature data, a decision may bemade on the impact on the product quality. These generate reports whichcan be used as the validation sets (706).

If the model yields the same decisions as the client, it is considered avalidated model and can be used in the production environment (710). Ifit results different decisions than expected from the client, a rootcause analysis may be conducted (707). The root cause analysis willdetermine if the decision rules are faulty, if the client is notfollowing their evaluation tools, or if there is a missing parameter inthe decision model. If the decision rules match the client decisionmodel, but the client has made different decisions in the past, themodel is still considered validated and the client will change theirevaluation tools to conform with the model (708).

Pseudo Geometry (FIG. 8 )

Using conventional geometry, modeling a thermal package's heat transferis a non-trivial four dimensional partial differential equation. Thepresent disclosure provides a solution by first creating apseudo-geometry that simplifies the problem. The pseudo geometry assumesthere are three heat transfer processes in the thermal package: productto PCM, ambient to product, and ambient to PCM. For each of the threeheat transfer processes, the solution of the partial differentialequation is posited to be a first order plus dead time (FOPDT) model. Ina FOPDT model, there are three coefficients: the gain, time constant,and dead time. These change as the PCM in the thermal package changephase. As a result, the heat transfer processes are modeled bysimultaneously solving the three FOPDT models and adjusting theconstants for subcooled PCMs, PCMs that are changing phase, and PCMsthat have fully changed phase. In the model structure there is aconditional switch (stage decider) which determines which stage thepackage model is in. This switch evaluates the heat flowing in and outof the PCM to determine if they have changed phase or not. This pseudogeometry can work with multiple phase change materials with differentphase change temperatures.

FIG. 8 describes an example case of the pseudo geometry that is used indevelopment of the packaging model 104. At 801, the package model 104 isprovided product temperature and lane temperature data sets from realshipments. The parameters of the equations involved in the pseudogeometry are attuned to the container, the loading, and the servicelevel of the shipment. In addition, in the example case there aretypically three stages to any particular shipment which is governed bythe state of the PCM. There is the subcooled stage (stage 1), where thePCM has not begun to change phase. There is the melting stage (stage 2),where the PCM is changing phase. There is the melted stage (stage 3),where the PCM is past its phase change point. The actual model evaluatesthe equations based on a separate calculation that decides which stagethe system is in.

The model parameters are optimized for each individual stage, as eachstage has slightly different heat transfer characteristics. If the modeldoes not perform well, additional data is collected to help characterizethe system.

In a different example case, the model can analyze a system that doesnot contain PCM and instead uses active cooling. A refrigerated systemcan still be characterized by the heat transfer pathways, but withdifferent parameters. The product can be in a refrigerated trailer,directly exposed to the air. In this circumstance the producttemperature can still be evaluated, it will just be very similar or thesame as the lane temperature.

The development of the package model not only identifies the temperatureof the product in the container, but also identifies the operationalvariability of the container. This variability is something that isinherent in almost every process, and is the result of minormanufacturing differences, minor differences in human operation, orother seemingly insignificant factors. This variability for thecontainer is used later in the decision model

The package model 104 is built using a pseudo geometry to evaluate thetemperature of the product. The pseudo geometry analyses theinteractions between components instead of the components themselves todetermine the product temperature. In an example case, there can bethree sources or sinks for heat transfer in a typical container; thephase change material (PCM), the outside air temperature (ambient), andthe product. In a typical simulation these components are all placed inthe specific spots where they would be in reality and given propertiesof the components such as their thermal conductivity, density, overallmass, and other properties. In the pseudo geometry the placement andindividual properties are largely ignored, and the focus is on theinteractions of the components, which can be described by a simple firstorder plus dead time (FOPDT) function:

${T(s)} = \frac{Ke^{\theta}}{{\tau s} + 1}$

T is the temperature of the product at a particular time (s). K is thegain of the system, which in this case is always 1 and is ignored. θ isthe dead time, which is the delay before the temperature is affected bythe heat transfer. τ is the time constant, which is a number thatdescribes how quickly the temperature changes after it is exposed tosomething that is trying to change it. This equation applies to each ofthe individual heat transfer pathways, and each pathway has its ownparameters. In the example case, there would be three heat transferpathways:

-   -   Ambient <-> Product (803);    -   Ambient <-> PCM (802); and    -   PCM <-> Product (804).

The pseudo geometry contains a stage deciding switch, which determinesthe state of the PCM in the system. In an example case there are threestages to a container. Stage 1 is a consistent time delay for mostcontainers, often referred to as the “equilibration time” of thecontainer. This time is where materials are getting to the temperatureat which they will be for most of the shipment. When the stage decideris evaluating at the beginning of a shipment, it is often set to justuse the time delay characteristic for a container. Stage 2 and Stage 3of the container are evaluations of the system before and after the PCMchanges phase. The PCM in a container reacts to heat the same way thatany ice does; if it is exposed to enough heat it will melt, but if it iscooled down after that, it will refreeze. The stage decider monitors theheat into the system and determines when the PCM changes phase, but italso evaluates if the heat transfer out of the system is enough tochange its phase back. This is a simplified case as there may bemultiple PCMs in a container with very different properties, and therecould potentially be more stages based on that circumstance.

Stage 2 and stage 3 of the decider is evaluated by calculating heat intoor out of the system. The example case in FIG. 8 contains a single PCM,but it is not uncommon for there to be multiple different PCMs in asingle container. This stage decider considers the heat flowing into orout of the system over time and the thermodynamic properties of the PCM.The equation that describes this calculation is below:

ΔH _(system)(t)=∫_(t1) ^(t2) T(t)−T _(phase change)

where:

-   -   ΔH(t) is the heat change in the system    -   t is time, with t₂ being the final time and t₁ being the start        time    -   T(t) is the ambient temperature at a given time    -   T_(phase change) is the temperature at which a PCM changes phase

The phase change temperature is constant because all energy going intoor out of the system contributes solely to the energy needed to changephase at that temperature, and not to changing the temperature of thePCM.

The PCMs in a container will have consistent properties across everyshipment, and it is easily determined where they have changed phase byevaluating the second derivative of the temperature data from previousshipments. When the inflection of the curve changes, that is a pointwhere all the PCM has changed phase. This time point is then used in theequation to calculate the total heat that flowed into the system beforeit finished changing phase. The total heat that has flowed into or outof the system is then known and is set as a consistent property for thatcontainer. When a container is shipped in reality this same value isused. The total heat into or out of the system is calculated at everystep, and when it exceeds the predetermined value, the package modelchanges which equations are used to evaluate temperature. Once thesystem is well characterized, the model is implemented in the productionenvironment.

Interpolation of Simple System Coefficients to Determine UnknownComplicated Behavior

In an example case, any one particular packaging system heat transferpathway may be governed by a simple equation with only two variablecoefficients.

${T(s)} = \frac{e^{\theta}}{{\tau s} + 1}$

When the entire packaging system is combined for evaluation theresulting equation can potentially have more than a dozen coefficients.However, the overall complicated system is still composed of thosesimple systems. The extra coefficients are in actuality differentcombinations of the coefficients from the simple systems. The combinedequations can be easily represented by the form:

T _(product)(s)=(T _(PCM to Product)(s))(T _(Ambient to PCM)(s))+(T_(Ambient to Product)(s))

The above may be expanded to capture all variables and is represented bythe form:

${\tau_{product}(s)} = \left( \frac{{e^{\theta_{1}}{e^{\theta_{2}}\left( {{\tau_{3}s} + 1} \right)}} + {{e^{\theta_{3}}\left( {{\tau_{1}s} + 1} \right)}\left( {{\tau_{2}s} + 1} \right)}}{\left( {{\tau_{1}s} + 1} \right)\left( {{\tau_{2}s} + 1} \right)\left( {{\tau_{3}s} + 1} \right)} \right)$

where a subscript of 1 is for the PCM to product pathway, a subscript of2 is for the ambient to PCM pathway, and a subscript of 3 is for theambient to product pathway.

The coefficients used in the package model use this property todetermine the behavior of packages with loadings that have not beentested. In an example case, a package model may be characterized byusing data from shipments of the minimum and maximum loading. Theseexamples would have different coefficients for the τ and θ variables. Ifthe model was queried for the behavior of a package loaded with productbetween these two amounts, there may not be data to directlycharacterize it. The model can interpolate the coefficients (τ and θ)from the simple systems in minimum and maximum loading equations todetermine the behavior for any point in between the validated data sets.

Example Cases

As an example case on how the overall process would work, the systemwould begin with a client providing data on their available containers.When the client is ready to make a shipment, they can query the systemto make an evaluation. The client specifies origin and destination, andthe system generates a set of scenarios from day zero to sometime in thefuture (fourteen days) using a preset of packages (heavily insulated,moderately insulated, and lightly insulated) and shipping service levels(next day, two day, and ground). The system will use weather data togenerate an estimate of the lane temperature for each shipment scenario.Then, the system will evaluate each of the client's containers againstthe lane temperatures. This will provide an estimated producttemperature, along with a statistical analysis on how accurate theestimate is for each scenario (14×3×3 or 126 in this example). This isfinally translated into a risk chart, where the client may be given achart with red (high risk), yellow (medium risk), and green (low/norisk) rankings. The process from start to end will only take a fewminutes. Typically, an overdesigned solution would be used, but theclient may see that another design that is much cheaper has little/norisk to the product.

In an example case, a shipment in January is scheduled that needs tomaintain temperatures between 35° F. and 46° F. The client has a “wintercontainer” used during this time of year, and is a 24-hour durationcontainer which is designed to prevent the product from freezing duringcolder months. This container has extra PCM in it to prevent the productfrom freezing.

The client queries the system to run a set of scenarios for the nextweek with the available containers, service levels, on each day of theweek. That set of scenarios determines that it will beuncharacteristically cold (<−20° F.) during days 1 and 2 of the week,and every container option shows a high-level risk of the productgetting too cold. It also determines on day 3 of the week that thetemperatures are about average for that time of year (^(˜)30° F.), andthe winter containers have a medium level risk of the product gettingtoo cold. On day 4 of the week, the model determines it will beuncharacteristically warm with forecasted temperatures above 60° F. atboth the origin and destination. The system determines that there is ahigh level risk of the product getting too warm in the winter container.

However, the “summer container” used by this client has less PCM, andhas a low level risk of the product getting too warm or cold in thisparticular scenario. It also shows that because there is a mild outsidetemperature (60° F.) and not the extreme temperatures the box wasdesigned for (>90° F.), the summer box can be shipped via 2-day shippinginstead of overnight shipping with no added risk. The client can use thesummer container in January, with lower cost due to reduced weight, lessmaterials, and cheaper service level, while simultaneously reducing therisk that the product will go out of temperature.

In a different example case, the client may have a container that didnot include a temperature monitor when it should have, but they need toknow if the product's temperature was maintained. Under normalcircumstances, this product would need to be discarded or used “at risk”with a patient because there is no way to evaluate impact to productquality. The client knows the container, origin, destination, andapproximately when it was shipped. The evaluation and risk system can bequeried to give an estimation of the product temperature during theshipment to determine if it maintained temperature. If it did notmaintain temperature, there is still a good estimation of how long itspent at different temperatures, which allows the manufacturer todetermine the impact of the excursion on the product quality. Theproduct potentially can be saved and given to a patient with no risk tosafety, and the manufacturer is not required to pay for replacing theproduct.

It should be understood that the various techniques described herein maybe implemented in connection with hardware or software or, whereappropriate, with a combination of both. Thus, the methods and apparatusof the presently disclosed subject matter, or certain aspects orportions thereof, may take the form of program code (i.e., instructions)embodied in tangible media, such as floppy diskettes, USB drives,CD-ROMs, hard drives, or any other machine-readable storage mediumwherein, when the program code is loaded into and executed by a machine,such as a computer, the machine becomes an apparatus for practicing thepresently disclosed subject matter. In the case of program codeexecution on programmable computers, the computing device generallyincludes a processor, a storage medium readable by the processor(including volatile and non-volatile memory and/or storage elements), atleast one input device, and at least one output device.

One or more programs may implement or utilize the processes described inconnection with the presently disclosed subject matter, e.g., throughthe use of an application programming interface (API), reusablecontrols, or the like. Such programs may be implemented in a high levelprocedural or object-oriented programming language to communicate with acomputer system. However, the program(s) can be implemented in assemblyor machine language, if desired. In any case, the language may be acompiled or interpreted language and it may be combined with hardwareimplementations.

Although the subject matter has been described in language specific tostructural features and/or methodological acts, it is to be understoodthat the subject matter defined in the appended claims is notnecessarily limited to the specific features or acts described above.Rather, the specific features and acts described above are disclosed asexample forms of implementing the claims.

1-18. (canceled)
 19. A method modeling a thermal package's heattransfer, comprising: using a pseudo-geometry that represents three heattransfer processes in a thermal package that include (1) product tophase change material (PCM), (2) ambient temperature to product, and (3)ambient temperature to PCM; and for each of the three heat transferprocesses: positing a solution of a partial differential equation as afirst order plus dead time (FOPDT) model having a gain coefficient, atime constant, and a dead time that change as the PCM in a thermalpackage change phase; simultaneously solving models associated with eachof the three heat transfer processes and adjusting constants associatedwith the gain coefficient, the time, and the dead time constants forsubcooled PCM, PCMs that are changing phase, and PCMs that have fullychanged phase; and using a result to generate a package model thatreceives product temperature specifications and lane temperature data todetermine an optimal packaging from a predetermined set of packing to beused for a shipment of the product.
 20. The method of claim 19, whereinthe package model determines if it is tuned to model a subcooled stagewherein the PCM has not begun to change phase, a melting stage whereinthe PCM is changing phase, and a melted stage wherein the PCM is pastits phase change point.
 21. The method of claim 20, wherein modelparameters are optimized for each of the subcooled stage, the meltingstage, and the melted stage, and wherein each stage has different heattransfer characteristics.
 22. The method of claim 19, wherein thepseudo-geometry analyses interactions between components to determinethe product temperature.
 23. The method of claim 22, wherein theinteractions are described by the FOPDT model, as follows:${T(s)} = \frac{Ke^{\theta}}{{\tau s} + 1}$ wherein T is the temperatureof the product at a particular time (s), wherein K is the gain of asystem, wherein Θ is the dead time that is a delay before thetemperature is affected by the heat transfer, and wherein τ is the timeconstant that describes how quickly the temperature changes after it isexposed to something that is trying to change it.
 24. The method ofclaim 19, wherein the FOPDT model is applied to individual heat transferpathways and each pathway has its own parameters.
 25. The method ofclaim 24, wherein the individual heat transfer pathways comprise:Ambient-Product; Ambient-PCM; and PCM-Product.
 26. The method of claim25, further comprising defining a system as a composition of theindividual heat transfer pathways represented by:T _(product)(s)=(T _(PCM to Product)(s))(T _(Ambient to PCM)(s))+(T_(Ambient to Product)(s)).
 27. The method of claim 26, wherein thesystem is further defined as:${\tau_{product}(s)} = \left( \frac{{e^{\theta_{1}}{e^{\theta_{2}}\left( {{\tau_{3}s} + 1} \right)}} + {{e^{\theta_{3}}\left( {{\tau_{1}s} + 1} \right)}\left( {{\tau_{2}s} + 1} \right)}}{\left( {{\tau_{1}s} + 1} \right)\left( {{\tau_{2}s} + 1} \right)\left( {{\tau_{3}s} + 1} \right)} \right)$wherein a subscript of 1 is for the PCM to product pathway, a subscriptof 2 is for the ambient to PCM pathway, and a subscript of 3 is for theambient to product pathway.
 28. The method of claim 19, furthercomprising determining a stage of the PCM in a system using thepseudo-geometry.
 29. The method of claim 28, wherein there are threestages to a container, wherein stage 1 is a consistent time delay wherematerials are getting to the temperature at which they will be for mostof the shipment, and wherein stage 2 and stage 3 are evaluations of thesystem before and after the PCM changes phase.
 30. The method of claim29, further comprising determining the heat flowing into or out of thesystem over time in stage 2 or stage 3 in accordance with:ΔH _(system)(t)=∫_(t1) ^(t2) T(t)−T _(phase change) wherein: ΔH(t) isthe heat change in the system, t is time, with t₂ being the final timeand t₁ being the start time, T(t) is the ambient temperature at a giventime, and T_(phase change) is the temperature at which a PCM changesphase.
 31. The method of claim 27 further comprising, applying thefollowing for package election:PSRu=∫ _(t1) ^(t2) T _(uspec) −T(t)dtPSRl=∫ _(t1) ^(t2) T(t)−T _(lspec) dt wherein PSRu is upper packagesuitability rating, and wherein PRl is lower package suitability rating